Question

A medical plan requires a patient to pay a $25.00 copay plus 20% of all charges incurred for a medical procedure. If the average bill for a patient is between $200 and $800, find the range of the original bill.

Answer 1

Let the original bill be
`x`, then the final bill after the charges been added are
`1.2x+25`, where
`1.2` is the increase in the bill by 0.2 (100%+20% = 120% = 1.2)

The range of the original bill is
200 <
`1.2x+25` < 800, subtract each term by 25
175 <
`1.2x` < 775, divide each term by
`1.2`
145.83 <
`x` < 645.83

Hence, the range of the original bill is between $145.83 and $645.83